Can you revive dead-weight employees?

FORTUNE — Your company is probably carrying dead weight, though it might not be where you think.

Managers often harbor the fear that employees with one foot out the door will lose motivation to work hard at their current jobs, and that’s a real problem: more and more people want to leave their jobs today than in years past. Between 2005 and 2010, the number of people who said they were seriously considering leaving their job jumped from 23% to 32%, according to new research from consulting firm Mercer.

“HR departments are very concerned,” says Dave Van De Voort, a human resources consultant at Mercer. “As their competitors start to hire, it’s going to be very tough to keep people from leaving, and it will be the best people with the best training that will go.”

But employees on the way out aren’t actually as big of a threat to a healthy corporate culture as the growing ranks of disillusioned and frustrated workers who simply stay put.

Twenty-one percent of the people surveyed in the Mercer study said that they were apathetic about whether they stayed or left. But what’s worse is that this part of the employee population had significantly more negative things to say about their companies than both people who were staying and people who planned to leave.

The people within this 21% group are lingering at their jobs for a reason, says Van De Voort, who says that unproductive employees generally fall in one of two categories. The first includes people who are office favorites; they’re likeable, but bad at their jobs. Most of those were culled during job cuts throughout the recession. The second type, however, is still around. These are people with a necessary skill. They’re valuable, but they’re either unproductive or negative influences on others, largely because of the chips on their shoulders.

“You see very highly talented people that have really destructive behaviors, and the organization will tolerate them because they are so talented,” says Ken Oehler, a senior vice president at consulting firm Aon Hewitt.

A lot of these people have reasons to be upset. Many have seen their colleagues take pay cuts or lose their jobs. Others feel like their company’s management team hasn’t chosen the best course to adapt to tough times. Yet, because the economy is still uncertain, employees feel trapped, so they stay, and their negative attitudes fester.

“One of my folks refers to them as viruses,” Van De Voort says. “They’re truly causing harm, and employers need to have a plan for either helping these people leave or getting them to be more engaged.”

The question is how, and that can be tricky. First, you have to root out the people who are checking out or otherwise negatively affecting the organization. That part is easier than you may think, says Jon Katzenbach, a senior partner at consulting firm Booz & Company. To find them, you have to use their foils – the key motivators in a company. These are often informal leaders who are not necessarily at the top of a company’s hierarchy.

“You’re looking for someone whose colleagues would walk over hot coals for them,” says Katzenbach. Those are the first people a manager should ask about dissatisfied employees. And if these key motivators are the disengaged ones themselves, they are the most important to win over.

The first step towards winning back disengaged employees is to ensure that they have productive, one-on-one conversations with supervisors or management. You have to find out why people aren’t motivated. If they’ve lost interest for a good reason, the company can often make small adjustments to bring them back on board.

Even behavior that seems unworkable on the surface can be useful, says Kristin Behfar, a professor of business administration at the University of Virginia’s Darden School of Business. Behfar says she once worked with a team of people that complained to her about one of the members, an experienced employee who had grown frustrated with the company. His negative attitude was poisoning the rest of the team, but they needed him.

Behfar says she asked them what the team members thought this employee was good at, and they said he had a talent for dishing out criticism. So they put his skill to use. The group made him in charge of reviewing all outgoing work for errors, giving his critical eye a purpose, with great results. “I love that story,” Behfar says. “He cared, but the circumstances he was in left him unengaged.” Experienced people like the man in this example are pivotal dead-weight turnaround targets.

Of course, the best way to keep your staff engaged is to stay on top of the issue from the hiring process on, says Stephen Coco, a consultant with Buck. Have a formal employee orientation program and keep up with staffers as they grow within the company. As they develop, create regular opportunities for them to give feedback, and make sure that managers have solid relationships with their employees.

But a struggling or changing company may have to respond directly to an engagement problem. In that case, you want to encourage specific changes from certain people, says Katzenbach, not overhaul the entire culture. “This is a rifle game, not a shotgun game,” he says.